Method for including an implicit integrity or authenticity check into a white-box implementation

ABSTRACT

A method of performing a cryptographic operation using a cryptographic implementation in a cryptographic system, including: receiving, by the cryptographic system, an identifying string value; receiving, by the cryptographic system, an input message; performing, by the cryptographic system, a keyed cryptographic operation mapping the input message into an output message wherein the output message is the correct result when the identifying string value equals a binding string value.

TECHNICAL FIELD

Various exemplary embodiments disclosed herein relate generally toincluding an implicit integrity or authenticity check into a white-boximplementation.

BACKGROUND

The Internet provides users with convenient and ubiquitous access todigital content. Because the Internet is a powerful distributionchannel, many user devices strive to directly access the Internet. Theuser devices may include a personal computer, laptop computer, set-topbox, internet enabled media player, mobile telephone, smart phone,tablet, mobile hotspot, or any other device that is capable of accessingthe Internet. The use of the Internet as a distribution medium forcopyrighted content creates the compelling challenge to secure theinterests of the content provider. Increasingly, user devices operateusing a processor loaded with suitable software to render (playback)digital content, such as audio and/or video. Control of the playbacksoftware is one way to enforce the interests of the content ownerincluding the terms and conditions under which the content may be used.Previously many user devices were closed systems. Today more and moreplatforms are partially open. Some users may be assumed to have completecontrol over and access to the hardware and software that providesaccess to the content and a large amount of time and resources to attackand bypass any content protection mechanisms. As a consequence, contentproviders must deliver content to legitimate users across a hostilenetwork to a community where not all users or user devices can betrusted.

Secure software applications may be called upon to carry out variousfunctions such as, for example, cryptographic functions used to protectand authenticate digital content. In order to counter attacks, thesealgorithms have to be obfuscated (hidden) in order to prevent reverseengineering and modification of the algorithm or prohibit obtaining theuser-specific secure information. Accordingly, the functions of thesecure software application may be carried out by various functions asdefined by the instruction set of the processor implementing the securesoftware. For example, one way to obscure these functions is by the useof lookup tables.

The widespread use of digital rights management (DRM) and other securesoftware has given rise to the need for secure, tamper-resistantsoftware that seeks to complicate tampering with the software. Varioustechniques for increasing the tamper resistance of software applicationsexist. Most of these techniques are based on hiding the embeddedknowledge of the application by adding a veil of randomness andcomplexity in both the control and the data path of the softwareapplication. The idea behind this is that it becomes more difficult toextract information merely by code inspection. It is therefore moredifficult to find the code that, for example, handles access andpermission control of the secure application, and consequently to changeit.

As used herein, white-box cryptography includes a secure softwareapplication that performs cryptographic functions in an environmentwhere an attacker has complete control of the system running thewhite-box cryptography software. Thus, the attacker can modify inputsand outputs, track the operations of the software, sample and monitormemory used by the software at any time, and even modify the software.Accordingly, the secure functions need to be carried out in a mannerthat prevents the disclosure of secret information used in the securefunctionality. White-box cryptography functions may be implemented invarious ways. Such methods include: obscuring the software code; usingcomplex mathematical functions that obscure the use of the secretinformation; using look-up tables; using finite state machines; or anyother methods that carry out cryptographic functions but hide the secretinformation needed for those secure functions. A white-boximplementation may also contain components that include anti-debuggingand tamper-proofing properties.

There are several reasons for preferring a software implementation of acryptographic algorithm to a hardware implementation. This may, forinstance, be the case because a software solution is renewable if thekeys leak out, because it is has lower cost, or because theapplication-developer has no influence on the hardware where thewhite-box system is implemented.

SUMMARY

A brief summary of various exemplary embodiments is presented below.Some simplifications and omissions may be made in the following summary,which is intended to highlight and introduce some aspects of the variousexemplary embodiments, but not to limit the scope of the invention.Detailed descriptions of an exemplary embodiment adequate to allow thoseof ordinary skill in the art to make and use the inventive concepts willfollow in later sections.

Various exemplary embodiments relate to a non-transitorymachine-readable storage medium encoded with instructions for executionby a cryptographic implementation in a cryptographic system forperforming a cryptographic operation, the non-transitorymachine-readable storage medium including: instructions for receiving,by the cryptographic system, an identifying string value; instructionsfor receiving, by the cryptographic system, an input message;instructions for performing, by the cryptographic system, a keyedcryptographic operation mapping the input message into an output messagewherein the output message is the correct result when the identifyingstring value equals a binding string value.

Various embodiments are described wherein the output message is anincorrect result when the identifying string does not equal the bindingstring value.

Various embodiments are described wherein the identifying string valueis based upon an identification of the cryptographic implementation.

Various embodiments are described wherein the identifying string valueis based upon a hash of a Various embodiments are described wherein theidentifying string value is based upon an identification of thecryptographic system.

Various embodiments are described wherein the identifying string valueis based upon a user password.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the non-transitory machine-readable storage medium furtherincludes: instructions for encoding an output of the first functionbased upon the identifying string value; and instructions forinstructions for performing the second function on the encoded output ofthe first function wherein the second function includes decoding theencoded output of the first function using the binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and asecond function, and the non-transitory machine-readable storage mediumfurther includes: instructions for perturbing an output of the firstfunction using the identifying string value; and instructions forperforming the second function on the perturbed output of the firstfunction wherein the second function includes compensating for theperturbation of the output of the first function using the bindingstring value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the non-transitory machine-readable storage medium furtherincludes: instructions for introducing a perturbation in the calculationof the first function based upon the identifying string value;instructions for compensating for the perturbation in the calculation ofthe first function during calculation of the second function based uponthe binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the non-transitory machine-readable storage medium furtherincludes: instructions for introducing a perturbation in the calculationof the first function based upon the binding string value; instructionsfor compensating for the perturbation in the calculation of the firstfunction during calculation of the second function based upon theidentifying string value.

Various embodiments are described wherein the cryptographic systemincludes a network of finite state machines.

Various embodiments are described wherein the cryptographic systemincludes a network of lookup tables.

Various embodiments are described wherein the cryptographic operation isone of advanced encryption system (AES) or data encryption standard(DES).

Further, various exemplary embodiments relate to a method of producing acryptographic implementation of a cryptographic operation mapping aninput message to an output message in a cryptographic system that bindsthe cryptographic implementation to a binding string value, including:receiving information specifying the binding string value; modifying acryptographic implementation to receive a identifying string value;modifying the cryptographic implementation based upon the receivedinformation specifying the binding string value so that: when a receivedidentifying string value is equal to the binding string value, thecryptographic implementation outputs a correct output message.

Various embodiments are described wherein when a received identifyingstring value is not equal to the binding string value, the cryptographicimplementation outputs an incorrect output message.

Various embodiments are described wherein the identifying string valueis based upon an identification of the cryptographic implementation.

Various embodiments are described wherein the identifying string valueis based upon a hash of a portion of the cryptographic implementation.

Various embodiments are described wherein the identifying string valueis based upon an identification of the cryptographic system.

Various embodiments are described wherein the identifying string valueis based upon a user password.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and modifying the cryptographic implementation so that: theoutput of one of the first function is encoded based upon theidentifying string value; and a second function is performed on theencoded output of the first function wherein the second functionincludes decoding the encoded output of the first function using thebinding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and modifying the cryptographic implementation so that: theoutput of one of the first function is perturbed using the identifyingstring value; and a second function is performed on the encoded outputof the first function wherein the second function includes compensatingfor the perturbation of the output of the first function using thebinding string value with.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and modifying the cryptographic implementation so that: aperturbation is introduced in the calculation of the first functionbased upon the identifying string value; the perturbation is compensatedfor in the calculation of the first function during calculation of thesecond function based upon the binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and modifying the cryptographic implementation so that: aperturbation is introduced in the calculation of the first functionbased upon the binding string value; the perturbation is compensated forin the calculation of the first function during calculation of thesecond function based upon the identifying string value.

Various embodiments are described wherein the cryptographic systemincludes a network of finite state machines.

Various embodiments are described wherein the cryptographic systemincludes a network of lookup tables.

Various embodiments are described wherein the cryptographic operation isone of advanced encryption system (AES) or data encryption standard(DES).

Further, various exemplary embodiments relate to a method of performinga cryptographic operation using a cryptographic implementation in acryptographic system, comprising: receiving, by the cryptographicsystem, an identifying string value; receiving, by the cryptographicsystem, an input message; performing, by the cryptographic system, akeyed cryptographic operation mapping the input message into an outputmessage wherein the output message is the correct result when theidentifying string value equals a binding string value.

Various embodiments are described wherein the output message is anincorrect result when the identifying string does not equal the bindingstring value.

Various embodiments are described wherein the identifying string valueis based upon an identification of the cryptographic implementation.

Various embodiments are described wherein the identifying string valueis based upon a hash of a portion of code in the cryptographic system.

Various embodiments are described wherein the identifying string valueis based upon an identification of the cryptographic system.

Various embodiments are described wherein the identifying string valueis based upon a user password.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the method further comprises: encoding an output of thefirst function based upon the identifying string value; and performingthe second function on the encoded output of the first function whereinthe second function includes decoding the encoded output of the firstfunction using the binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and asecond function, and the method further comprises: perturbing an outputof the first function using the identifying string value; and performingthe second function on the perturbed output of the first functionwherein the second function includes compensating for the perturbationof the output of the first function using the binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the method further comprises: introducing a perturbationin the calculation of the first function based upon the identifyingstring value; compensating for the perturbation in the calculation ofthe first function during calculation of the second function based uponthe binding string value.

Various embodiments are described wherein cryptographic implementationincludes a plurality of functions including a first function and secondfunction, and the method further comprises: introducing a perturbationin the calculation of the first function based upon the binding stringvalue; compensating for the perturbation in the calculation of the firstfunction during calculation of the second function based upon theidentifying string value.

Various embodiments are described wherein the cryptographic systemincludes a network of finite state machines.

Various embodiments are described wherein the cryptographic systemincludes a network of lookup tables.

Various embodiments are described wherein the cryptographic operation isone of advanced encryption system (AES) or data encryption standard(DES).

BRIEF DESCRIPTION OF THE DRAWINGS

In order to better understand various exemplary embodiments, referenceis made to the accompanying drawings, wherein:

FIG. 1 illustrates the main steps of a round of AES;

FIG. 2 illustrates a white-box AES implementation with encodings on theinput of the rounds;

FIG. 3 illustrates the computation of one output nibble by means of anetwork of look-up tables;

FIG. 4 illustrates a portion of the network table of FIG. 3 obfuscatedby encoding the inputs and outputs; and

FIG. 5 illustrates a first embodiment of binding a white-boximplementation;

FIG. 6 illustrates the application of obfuscation to the white-boximplementation of FIG. 5;

FIG. 7 illustrates a second embodiment of binding a white-boximplementation;

FIG. 8 illustrates a third embodiment of binding a white-boximplementation; and

FIG. 9 is a flow chart illustrating a method of binding a white-boximplementation to a binding string.

To facilitate understanding, identical reference numerals have been usedto designate elements having substantially the same or similar structureand/or substantially the same or similar function.

DETAILED DESCRIPTION

The description and drawings illustrate the principles of the invention.It will thus be appreciated that those skilled in the art will be ableto devise various arrangements that, although not explicitly describedor shown herein, embody the principles of the invention and are includedwithin its scope. Furthermore, all examples recited herein areprincipally intended expressly to be for pedagogical purposes to aid thereader in understanding the principles of the invention and the conceptscontributed by the inventor(s) to furthering the art, and are to beconstrued as being without limitation to such specifically recitedexamples and conditions. Additionally, the term, “or,” as used herein,refers to a non-exclusive or (i.e., and/or), unless otherwise indicated(e.g., “or else” or “or in the alternative”). Also, the variousembodiments described herein are not necessarily mutually exclusive, assome embodiments can be combined with one or more other embodiments toform new embodiments.

The discussion below is directed to white-box cryptography because it isthe most challenging attack model. Further, many cryptographicimplementations are deployed and used in an environment where they aresubject to a white-box attack. There is also a black-box attack modeland a grey-box attack model. In the black-box attack model, it isassumed that the attacker only has access to the input and output of theimplementation. In the grey-box attack model, it is assumed, that inaddition the access to the input and the output of the implementation,that the attacker has access to side channel information regarding theexecution of the implementation. Such side channel information mayinclude power, timing, electronic emissions, etc. Accordingly, thebenefits of the embodiments described below may be used to prevent anyof these various levels of attack as well as others that may be defined.Therefore, where white-box implementations are described, it is intendedthat they may include black-box implementations as well as grey-boximplementations that use the various methods described in theembodiments below.

Code lifting is a problem that may arise with a software implementationof cryptographic algorithm. This problem may be overcome by binding thewhite-box implementation to an arbitrary given string s, i.e., thewhite-box implementation only works properly if the string s isavailable. Binding the white-box implementation to a string s, may beused to implement node locking, software tamper resistance, userbinding, and traitor tracing. The problem of code lifting may arisebecause a software implementation of a cryptographic algorithm may becopied and used on unauthorized nodes or by unauthorized users.Accordingly, a white-box implementation, although it may effectivelyhide a cryptographic key, may still be distributed as a whole. Thiswhite-box implementation may be as valuable as the key itself. If, forinstance, the white-box implementation implements a decryptionalgorithm, then by not having the key, the receiver may not be able toencrypt, but the white-box implementation is sufficient to decrypt. Thismeans that an adversary illegitimately distributes the white-boximplementation as a whole instead of the underlying hidden cryptographickey, which typically is of high value that should not be distributed inan uncontrolled way. Typically, the key is only present implicitly. Inother embodiments, the key may include dynamic keys that, for example,take implicit key information and change it with some sort of dynamicinformation to change the key used in the cryptographic function.

As mentioned above the use of an arbitrary given string s may be used toovercome these problems. A solution for using an arbitrary given strings is described in U.S. Pat. No. 8,479,016 to Michiels (“Michiels”). Thestring s may be some binary string that may be derived from the deviceon which the white-box implementation should be running and that cannotbe derived on other devices. For instance, s may be defined as a uniqueidentifier of the device. In Michiels a white-box implementation isderived containing s, and this white-box implementation is placed on thedevice where the string s is omitted where the string is part of alookup table used in the white-box implementation. As a result, thedevice can only execute the white-box implementation once it can derivethe omitted string s and then uses the value of s when the table entryis requested that was omitted, i.e., the white-box implementation canonly be executed on the legitimate device.

Below embodiments are described that implement an alternative approachfor binding a white-box implementation to an arbitrary string s thanincluding it in the definition of a lookup table. Instead the string sis a parameter of a function of the white-box implementation, i.e., thestring s is not used for the specification of the function as inMichiels, but rather as a parameter of the function.

The embodiments described below are also useful for other strings s thatrepresent the integrity or authenticity of the system that the white-boximplementation runs on. If, for instance, s is the hash of some codefragment, then it hardens the software against tampering. Also, thestring s may be used for node locking where s is the uniqueidentification of a node or hardware in the white-box system. Anotheruse-case for the string s is traitor tracing. If the string is the nameof the legitimate owner of a white-box implementation, and if thiswhite-box implementation is encountered on an illegitimate device or onthe Internet, then the white-box implementation may be traced back tothe source of the leakage. Further, s may be used to identify a users bybeing associated with a user password or hash of a user password.

In order to demonstrate embodiments of the invention, an examplewhite-box implementation of AES will now be described. White-boxcryptography is the discipline of implementing a cryptographic algorithmin software such that it is difficult for an attacker to find the key.Hereby, the strongest conceivable (but for software most realistic)attack model is assumed in which the adversary is assumed to have fullcontrol over and full access to the white-box implementation.

A table-based approach to a white-box implementation of the AdvancedEncryption Standard (AES) and the Data Encryption Standard (DES) wereproposed in the following papers: “White-Box Cryptography and an AESImplementation”, by Stanley Chow, Philip Eisen, Harold Johnson, and PaulC. Van Oorschot, in Selected Areas in Cryptography: 9th AnnualInternational Workshop, SAC 2002, St. John's, Newfoundland, Canada,August 15-16, 2002, referred to hereinafter as “Chow 1”; and “AWhite-Box DES Implementation for DRM Applications”, by Stanley Chow,Phil Eisen, Harold Johnson, and Paul C. van Oorschot, in Digital RightsManagement: ACM CCS-9 Workshop, DRM 2002, Washington, D.C., USA, Nov.18, 2002, referred to hereinafter as “Chow 2”. Chow 1 and Chow 2disclose methods of using a table-based approach to hide thecryptographic key by a combination of encoding its tables with randombijections, and extending the cryptographic boundary by pushing it outfurther into the containing application.

As noted, for many cryptographic operations it is desired to have awhite-box implementation. The invention may be applied, for example, tosymmetric and asymmetric cryptographic operations. Also, the inventionmay be applied to block ciphers, stream ciphers, message authenticationschemes, signature schemes, etc. Note that the invention may also beapplied to hash functions. The latter is especially useful if the hashfunction is used as a building block which processes secret information,e.g., a secret key, secret data, etc. For example, the invention may beapplied to a hash function used in a keyed-Hash Message AuthenticationCode (HMAC or KHMAC). Well known block ciphers include: AdvancedEncryption Standard (AES), Secure And Fast Encryption Routine, (SAFER,and variants SAFER+ and SAFER++), Blowfish, Data Encryption Standard(DES), etc. A well known stream cipher is RC4. Moreover any block ciphercan be used as stream cipher using an appropriate mode of operation,e.g., Cipher feedback (CFB), Counter mode (CTR), etc.

The white-box implementation may be implemented using a plurality ofbasic blocks. The plurality of basic blocks is interconnected, in thesense that some of the blocks build on the outputs of one or more of theprevious blocks. A basic block may also be implemented in softwarerunning on a general purpose computer chip, e.g. a microprocessor. Forexample, a basic block may use a plurality of computer instructions,including arithmetical instructions, which together implement thefunctionality of the basic block. A widely used implementation for thebasic block is a look-up table. For example, Chow 1 and Chow 2 take thisapproach to implement the AES and DES block ciphers. A look-up tableimplementation includes a list which lists for possible input values, anoutput value. The input value may be explicit in the lookup table. Inthat situation the look-up table implementation could map a particularinput to a particular output by searching in the list of input valuesfor the particular input. When the particular input is found theparticular output is then also found. For example, the particular outputmay be stored alongside the particular input. Preferably, the inputvalues are not stored explicitly, but only implicitly. For example, ifthe possible inputs are a consecutive range, e.g. of numbers orbit-strings, the look-up table may be restricted to storing a list ofthe output values. A particular input number may, e.g., be mapped to theparticular output which is stored at a location indicated by the number.Further, finite state machines or code obfuscation may be used toimplement the white-box implementation.

For example, a look up table for a function may be created by computingthe output value of the function for its possible inputs and storing theoutputs in a list. If the function depends on multiple inputs theoutputs may be computed and stored for all possible combinations of themultiple inputs. Look-up tables are especially suited to implementnon-linear functions, which map inputs to output in irregular ways. Awhite-box implementation can be further obfuscated, as is explainedbelow, by applying to one or more of its look-up tables a fixedobfuscating input encoding and a fixed output encodings. The results ofapplying a fixed obfuscating input encoding and output encodings is thenfully pre-evaluated. Using this technique, a look-up table would bereplaced by an obfuscated look-up table which has the same dimensions,that it takes the same number input bits and produces the same number ofoutput bits. The input encoding and output encoding used in suchobfuscation are not explicit in the final white-box implementation.

The network of basic blocks are arranged to compute an output messagewhen they are presented with an input message. Typically, the inputmessage is operated upon by a number of basic input blocks. A number offurther basic blocks may take input from one or more of the basic inputblocks and/or from the input. Yet further basic blocks can take input inany combination of the input message, the output of basic input blocksand the output of the further basic blocks. Finally some set of basicexit blocks, i.e., at least one, produce as output all or part of theoutput-message. In this manner a network of basic blocks emerges whichcollectively computes the mapping from the input message to outputmessage.

The key used may be a cryptographic key and may contain sufficiententropy to withstand an anticipated brute force attack. It is noted thatin a white-box implementation, the key is typically not explicitlypresent in the implementation. This would risk the key being found byinspection of the implementation. Typically, the key is only presentimplicitly. Various ways are known to hide a key in a cryptographicsystem. Typically, at least the method of partial evaluation is used,wherein a basic block which needs key input is evaluated in-so-far thatit does not depend on the input-message. For example, a basic operationwherein an input-value, a masking value, which does not depend on theinput-message, e.g. a value from an S-box, and a key-value need to beXORed can be partially evaluated by XORing the key value and the maskingvalue together beforehand. In this way the operation still depends onthe key-value although the key-value is not explicitly present in theimplementation. Instead, only the XOR between the key-value andmasking-value is present in the implementation. Note that, morecomplicated ways and/or further ways of hiding the keys are compatiblewith this invention.

Below exemplary embodiments are described using the AES (AdvancedEncryption Standard) block cipher, because AES has become a widely usedstandard for block ciphers. AES is a block cipher with a block size of128 bits or 16 bytes. The plaintext is divided in blocks of 16 byteswhich form the initial state of the encryption algorithm, and the finalstate of the encryption algorithm is the cipher text. At any given pointin the encryption algorithm these 16 bytes are the state of theencryption algorithm. To conceptually explain AES, the bytes of thestate are organized as a matrix of 4×4 bytes. AES includes a number ofrounds, which depends on the key size. Each round is includes similarprocessing steps operating on bytes, rows, or columns of the statematrix, each round using a different round key in these processingsteps. In the discussion using AES as an example, it is noted that AESdefines a round in a specific manner. In the embodiments below, a roundis any grouping of steps that includes at least one non-linear mappingfunction, such as an S-box in AES. Accordingly, a round as describedbelow includes one non-linear mapping function and any combination ofother steps of the cryptographic function.

FIG. 1 illustrates some main processing steps of a round of AES. Theprocessing steps include:

AddRoundKey 110—each byte of the state is XORed with a byte of the roundkey;

SubBytes 120—a byte-to-byte permutation using a lookup table;

ShiftRows 140—each row of the state is rotated a fixed number of bytes;and

MixColumns 150—each column is processed using a modulo multiplication inGF(2⁸).

The steps SubBytes 120, ShiftRows 130, and MixColumns 150 areindependent of the particular key used. The key is applied in the stepAddRoundKey 110. Except for the step ShiftRows 140, the processing stepscan be performed on each column of the 4×4 state matrix withoutknowledge of the other columns. Therefore, they can be regarded as32-bit operations as each column consists of four 8-bit values. Dashedline 150 indicates that the process is repeated until the requirednumber of rounds has been performed.

Each of these steps or a combination of steps may be represented by alookup table or by a network of lookup tables. If the AddRoundKey 110step is implemented by XORing with the round key, then the key isvisible to the attacker in the white-box attack context. The AddRoundKey110 step can also be embedded in lookup tables, which makes it lessobvious to find out the key. In fact, it is possible to replace a fullround of AES by a network of lookup tables. For example, the SubBytes120, ShiftRows 130, and MixColumns 150 steps may be implemented usingtable lookups. Below a possible white-box implementation of AES insufficient detail is discussed to describe the embodiments of theinvention below, but further detailed descriptions of such animplementation are found in Chow 1. Also, other variations in the lookuptable implementation may be used which are within the scope of theinvention.

Both the table-based white-box implementations and the finite statemachine implementations have the property that all intermediate valuesin the implementation are encoded (as compared to a standardimplementation). Examples of white-box implementations using finitestate machines are disclosed in U.S. Patent Publication 2007/0014394entitled “Data Processing Method” and a presentation at the Re-trustSixth Quarterly Meeting entitled “Synchrosoft MCFACT™ Secure DataProcessing Technology” by Wulf Harder and Atis Straujums dated Mar. 11,2008, which each are hereby incorporated by reference for all purposesas if fully set forth herein. FIG. 2 illustrates a white-box AESimplementation with encodings on the input of the rounds, i.e., on theinput of the S-boxes. As shown, each of the 16 input bytes are encodedby f_(i) and each of the output bytes are encoded by g_(i).

In order to describe embodiments of the invention, a basic descriptionof a table-based white-box AES implementation will be described. For amore detailed description of a method for implementing a table-basedwhite-box AES see Chow 1. Chow 1 illustrates a specific implementationthat breaks up certain functions using tables of specified sizes. It iswell understood that various other divisions of the tables may be maderesulting in different functions for the look-up tables and differentsizes. Further, while the embodiments of the invention described belowuse a table-based white-box implementation of AES, other ciphers andcryptographic functions may be implemented according to the embodimentsdescribed. Also, other types of white-box implementations may be usedinstead of the table-base implementation, for example, a finite-stateimplementation.

The description of the table-based white-box AES is split into twosteps. In the first step, a round of AES is described as a network oflookup tables. In the second step, the tables are obfuscated by encodingtheir input and output.

Step 1: Implementing AES as a Network of Lookup Tables.

AES operates on data blocks of 16 bytes. These are typically describedas a 4×4 byte matrix, called the state including bytes x_(1,1), x_(1,2),x_(1,3), . . . x_(4,4). A round of AES as described above with respectto FIG. 1 include the following operations: AddRoundKey 110, SubBytes120, ShiftRows 130, and MixColumns 140. The first two operations,AddRoundKey and SubBytes can be merged into a single T-box operation.That is, we can define a byte-to-byte function T_(i,j) for input bytex_(i,j) as T_(i,j)(x_(i,j))=S(x_(i,j)⊕k_(i,j)) where k_(i,j) is a singlebyte of a 16 byte round key based upon the AES key. Let y_(i,j) be theoutput of T_(i,j). The ShiftRows operations is just an index-renumberingof the output bytes y_(i,j). For ease of presentation, this operation isomitted in this description, but may be incorporated into the look-uptable implementing T_(i,j) or implemented as a separate manipulation ofthe state matrix. In the MixColumns step, an output byte z_(i,j) of theround is computed from the 4 output bytes y_(1,j), y_(2,j), y_(3,j), andy_(4,j) via the algebraic expressionz_(l,j)=MC_(l,1)·y_(1,j)⊕MC_(l,2)·y_(2,j)⊕MC_(l,3)·y_(3,j)⊕MC_(l,4)·y_(4,j) in GF(2⁸) for some constants MC_(l,r).

Now define a lookup table for each byte-to-byte functionQ_(i,j,l)(x_(i,j))=MC_(l,i)·T_(i,j)(x_(i,j)) with i,j,l=1, 2, . . . ,16. Then any output byte z_(l,j) may be computed by XORing the resultsof these lookup tables, i.e.,z_(l,j)=Q_(1,j,l)(x_(1,j))⊕Q_(2,j,l)(x_(2,j))⊕Q_(3,j,l)(x_(3,j))⊕Q_(4,j,l)(x_(4,j)). Note that the index i,j,l ofQ-box can be interpreted as “the contribution of input byte i,j of around to output byte l,j of the round”. The XOR may be implemented tooperate on each of two nibbles (i.e., 4-bit values) as a lookup table toreduce the size of the XOR tables. Accordingly, the Q-box may beimplemented to produce output nibbles so that the size of the tables isreduced. Therefore, the computation of each output byte z_(l,j) of anAES-round has been described as a network of lookup tables. The networkof lookup tables to compute a single output nibble of byte z_(2,3) isshown in FIG. 3.

FIG. 3 illustrates the computation of one output nibble by means of anetwork of look-up tables. The superscript index (1) in the Q-boxesindicates that the tables only provide the first nibble of the output ofthe Q-box. A set of input bytes x_(1,3), x_(2,3), x_(3,3), and x_(4,3)in the input state 310 are input into the Q-boxes 320, 322, 324, 326.The outputs of lookup tables 320 and 322 are fed into the XOR 330, andthe outputs of lookup tables 324 and 326 are fed into the XOR 332. Theoutputs of XORs 330 and 332 are fed into XOR 334. The output of XOR 334is the first nibble of the output z_(2,3) of output state 340. Thesecond nibble of the output z_(2,3) of output state 340 may becalculated in the same way using additional Q-boxes along with a similarXOR network. Further, additional sets of tables may be implemented tocompletely convert the input state 310 into the output state 340 byreceiving a column of bytes from the input state and converting theminto the output of the corresponding column of the output state.

Step 2: Obfuscating the Tables and the Intermediate Values

In the implementation depicted in FIG. 3, the key may easily beextracted from the Q-boxes. Just applying the inverse MixColumnsmultiplication and the inverse S-box to the output reveals the plainAddRoundKey operation. To prevent this, the input and outputs of alllookup tables are encoded with arbitrary bijective functions. This isdescribed in Chow 1. This means that a lookup table is merged with anencoding function that encodes the output and with a decoding functionthat decodes the input. The encodings are chosen such that the outputencoding of one table matches the input encoding assumed in the nexttables. A portion of the implementation of FIG. 3 is depicted in FIG. 4for the first round. In this example, the input to the round is notencoded in order to be compliant with AES, but the output of the roundis encoded. The output encoding is handled in the next round. That is,unlike the first round, the second round (and the later rounds) assumesthat the input is encoded. Alternatively, the first round may receive anencoded input. This input encoding must then be applied elsewhere in thesoftware program containing the white-box implementation. Similarly, thelast round may or may not include an output encoding depending onwhether the output is to be AES compliant. Note that in the white-boximplementation obtained, both the lookup tables and the intermediatevalues are obfuscated.

The description of the table lookup based white-box implementationdescribed above was for the encryption operation of AES. It is notedthat the above description is easily adapted for the decryptionoperation by using the inverse of the SubBytes, ShiftRows, andMixColumns operations (invSubytes, invShiftRows, and invMixColumns).Accordingly, it is assumed that the description above can be used foreither the encryption or decryption operation of AES as needed in theembodiments below.

Embodiments are now described that let s be the parameter of a function(e.g., a lookup table) within the white-box implementation. That is, sis not used for the specification of the function, but as parameter ofthe function. In one embodiment, the internal encodings of intermediatevalues in the white-box implementation may be chosen in dependence of s.In another embodiment a dependence on s may be introduced in a computedvalue in the white-box implementation, which dependence is annihilatedfurther on in the computation so that the correct computed result may beobtained.

The method of introducing the dependence on an arbitrary string s maywork by parameterizing a white-box implementation with s. In atable-based white-box implementation, each lookup table has as inputeither the output (or part of the output) of another lookup table and/orthe input (or part of the input) of the implementation (e.g., theplaintext to be encrypted). Accordingly, lookup tables or functions areintroduced that have string s as their input.

As an example a single string s including 4 bits may bound to thewhite-box implementation. The string s may be called a binding stringvalue. This embodiment may easily be extended to larger bit strings byapplying the described method k times resulting in the binding ofstrings of 4 k bits.

FIG. 5 illustrates a first embodiment of binding a white-boximplementation. FIG. 5 is similar to FIG. 3, but includes an extensionto include binding the string s to the white-box implementation. Adependence on an arbitrary 4-bit string s may be implemented as follows.Let h₀, . . . , h₁₅ be 2⁴ bijective encoding functions, and let T be a8-to-4-bit lookup table 550 defined by T(v,σ)=h_(σ)(v) where v is anoutput nibble from the Q-box 520 and the nibble σ is an identifyingstring value. As can be seen in FIG. 5, the lookup table T 550 receivesthe input v from Q-box 520 Q⁽¹⁾ _(1,3,2), and the output of T 550 isinput into the succeeding XOR-table 530. The XOR-table 530 maycompensate for effect of T 550 on v when σ=s. This may be accomplishedby decoding the input to the XOR 530 using the function h_(s) ⁻¹. Whenσ=s this results in the correct value of v being input to the XOR 530.Otherwise, the value input to the XOR 530 is incorrect and results in anincorrect output of the white-box implementation. It is noted that theearlier the lookup table T is implemented in the white-boximplementation, the greater change it will have to the output when σ≠s.

FIG. 6 illustrates the application of obfuscation to the white-boximplementation of FIG. 5. Each of the Q-boxes 620, 622, 624, 626correspond to the Q-boxes in FIG. 5 but include input decodings g_(i)and output encodings f_(i) as shown. Further, the lookup table 650corresponds to the lookup table 550 in FIG. 5 but include input decodingf₁ ⁻¹ and output encoding f₈. Finally, the lookup XOR-tables 630, 632,634 correspond to the XOR-tables 530, 532, 534 in FIG. 5 but includeinput decodings f_(i) ⁻¹ and output encodings f_(i).

The embodiment described above is only guaranteed to work properly if itis provided with parameter σ=s. It is noted that by choosing thefunctions h₀, . . . , h₁₅ properly, different properties may berealized. The following are some examples. If the white-boximplementation is to run incorrectly for any string different from s andfor any execution of the white-box implementation, then this may berealized by defining h₀, . . . , h₁₅ such that for all v and i≠s itholds that h_(i)(v)≠h_(s)(v). If the white-box implementation is to runincorrectly for any string different from s, but if for a string i≠s thewhite-box implementation is to work incorrectly once in a while insteadof always (e.g., to make it more difficult for an adversary to detect),then we can choose to only have h_(i)(v)≠h_(s)(v) for some values of vinstead of all. For example, then h is chosen such thath_(i)(v)=h_(s)(v) for all i when the least significant bit of v is 1.This would result in about half of the values of v providing a correctoutput response, even when σ≠s.

FIG. 7 illustrates a second embodiment of binding a white-boximplementation. In this embodiment, an output of the first function inthe white-box implementation may be perturbed based upon σ or s. Then inan output of the second function, the perturbation may be compensatedfor using s or σ respectively. Let v₁,v₂,v₃,v₄ be the 4 nibbles computedby the 4 Q-tables 720, 722, 724, 726. To the value v₁ computed afterlookup table Q⁽¹⁾ _(1,3,2) 720 a value h(σ,v₁) is added via a lookuptable T₁ 750, where h is an arbitrary function with an 8-bit input and a4-bit output. Hence, T₁(σ,v₁)=v₁⊕h(σ,v₁). The idea is now how tocompensate for the addition of h(σ,v₁) when σ=s. This may beaccomplished as follows. After adding T₁ 750, the network computes thevalue v₁⊕v₂⊕v₃⊕v₄⊕h(σ,v₁), while v₁⊕v₂⊕v₃⊕v₄ should be computed. Tocompensate for this, a lookup table T₂ 752 and a XOR lookup table 736may be added, where T₂ computes the value h(s,v₁) and the XOR table addsh(s,v₁) to v₁⊕v₂⊕v₃⊕v₄⊕h(σ,v₁). This gives an implementation in which itis guaranteed that the proper value is calculated if and only if theimplementation receives the parameter σ=s. Again, the lookup tables inFIG. 7 may be obfuscated as described above to obtain a final white-boximplementation.

FIG. 8 illustrates a third embodiment of binding a white-boximplementation. It is noted that the function parameterized with s neednot be implemented by a lookup table. This third embodiment shows suchan implementation. The output v₁ of the table for Q⁽¹⁾ _(1,3,2) 820 isencoded by a function ƒ₁. Further, an encoding may be placed on top ofthis encoding ƒ₁ based on string s. More precisely, the value of anibble σ may be added to ƒ₁(v₁). Hence, v₁ is then encoded as⊕_(σ)∘ƒ₁(v₁), where ⊕_(σ) denotes the function that adds σ to itsargument. This function is not implemented by a lookup table but simplycomputed during run-time. This action may be compensated for in the nextXOR-table 830, where the decoding step ƒ₁ ⁻¹ is replaced by ƒ₁ ⁻¹∘⊕_(s)⁻¹. Again, this results in an implementation in which it is guaranteedthat the same functionality remains as before if and only if thewhite-box implementation is provide with the parameter σ=s.

A method according to the embodiments of the invention may beimplemented on a computer as a computer implemented method. Executablecode for a method according to the invention may be stored on a computerprogram medium. Examples of computer program media include memorydevices, optical storage devices, integrated circuits, servers, onlinesoftware, etc. Accordingly, a white-box system may include a computerimplementing a white-box computer program. Such system, may also includeother hardware elements including storage, network interface fortransmission of data with external systems as well as among elements ofthe white-box system.

In an embodiment of the invention, the computer program may includecomputer program code adapted to perform all the steps of a methodaccording to the invention when the computer program is run on acomputer. Preferably, the computer program is embodied on anon-transitory computer readable medium.

In addition to the computer program being implemented on anon-transitory computer readable medium, such computer program may betransmitted to a user or user device for installation and use. This maybe done over any communication network, for example, the internet.

Further, user devices implementing the embodiments described herein mayinclude, smart cards, payment cards, transit cards, access cards anddevices, mobile phones, tablets, personal digital assistants, portableand desktop computers, set-top boxes, digital video records, mediastreaming devices, etc. Uses of the embodiments described above mayinclude payment software, security access, parking access, transitaccess and payments, banking, software and digital media transmission,secure communications, content distribution, etc.

Further, because white-box cryptography is often very complicated and/orobfuscated it is tedious for a human to write. It is therefore ofadvantage to have a method to create the cryptographic system accordingto the embodiments of the invention in an automated manner.

A method of creating the cryptographic system according to the inventionmay be implemented on a computer as a computer implemented method, or indedicated hardware, or in a combination of both. Executable code for amethod according to the invention may be stored on a computer programmedium. In such a method, the computer program may include computerprogram code adapted to perform all the steps of the method when thecomputer program is run on a computer. The computer program is embodiedon a non-transitory computer readable medium.

FIG. 9 is a flow chart illustrating a method of binding a white-boximplementation to a binding string. First, the method begins 905. Then,a white-box implementation of the cryptographic operation is produced910. This may be produced as described above using various methods andimplementations. Next, information identifying a string s may bereceived 915. The string s may provide binding to a specific softwareinstance or a specific hardware system. Then, the white-boximplementation may be modified based upon the string s 920 so that: whenan input σ is received that equals the string s the white-boximplementation produces correct output for the cryptographic operationimplemented by the white-box implementation; and when an input σ isreceived that does not equal the string s the white-box implementationproduces an incorrect output for the cryptographic operation implementedby the white-box implementation. The various embodiments discussed aboveprovide different ways in which this capability may be implemented inthe white-box implementation. The method may then end 925.

Any combination of specific software running on a processor to implementthe embodiments of the invention, constitute a specific dedicatedmachine.

As used herein, the term “non-transitory machine-readable storagemedium” will be understood to exclude a transitory propagation signalbut to include all forms of volatile and non-volatile memory. Further,as used herein, the term “processor” will be understood to encompass avariety of devices such as microprocessors, field-programmable gatearrays (FPGAs), application-specific integrated circuits (ASICs), andother similar processing devices. When software is implemented on theprocessor, the combination becomes a single specific machine.

It should be appreciated by those skilled in the art that any blockdiagrams herein represent conceptual views of illustrative circuitryembodying the principles of the invention.

Although the various exemplary embodiments have been described in detailwith particular reference to certain exemplary aspects thereof, itshould be understood that the invention is capable of other embodimentsand its details are capable of modifications in various obviousrespects. As is readily apparent to those skilled in the art, variationsand modifications can be effected while remaining within the spirit andscope of the invention. Accordingly, the foregoing disclosure,description, and figures are for illustrative purposes only and do notin any way limit the invention, which is defined only by the claims.

What is claimed is:
 1. A non-transitory machine-readable storage mediumencoded with instructions for execution by a cryptographicimplementation in a cryptographic system for performing a cryptographicoperation, the non-transitory machine-readable storage mediumcomprising: instructions for receiving, by the cryptographic system, anidentifying string value; instructions for receiving, by thecryptographic system, an input message; instructions for performing, bythe cryptographic system, a keyed cryptographic operation mapping theinput message into an output message wherein the output message is thecorrect result when the identifying string value equals a binding stringvalue, wherein the keyed cryptographic function includes a first lookuptable that receives the identifying string and an intermediate value ofthe keyed cryptographic function and produces an encoded intermediatevalue based upon the identifying string, and wherein the keyedcryptographic function includes a second lookup table that receives theencoded intermediate value and produces a decoded intermediate valuebased upon the binding string value.
 2. The non-transitorymachine-readable storage medium of claim 1, wherein the output messageis an incorrect result when the identifying string does not equal thebinding string value.
 3. The non-transitory machine-readable storagemedium of claim 1, wherein the identifying string value is based upon anidentification of the cryptographic implementation.
 4. Thenon-transitory machine-readable storage medium of claim 1, wherein theidentifying string value is based upon a hash of a portion of code inthe cryptographic system.
 5. The non-transitory machine-readable storagemedium of claim 1, wherein the identifying string value is based upon anidentification of the cryptographic system.
 6. The non-transitorymachine-readable storage medium of claim 1, wherein the identifyingstring value is based upon a user password.
 7. The non-transitorymachine-readable storage medium of claim 1, wherein cryptographicimplementation includes a plurality of functions including a firstfunction producing the intermediate value and second function, and thenon-transitory machine-readable storage medium further comprises:instructions for performing the second function on the output of thefirst function wherein the second function includes decoding the outputof the first function using the binding string value.
 8. Thenon-transitory machine-readable storage medium of claim 1, whereincryptographic implementation includes a plurality of functions includinga first function producing the intermediate value and a second function,and the non-transitory machine-readable storage medium using theidentifying string value, further comprising: instructions forperforming the second function on the perturbed output of the firstfunction wherein the second function includes compensating for theperturbation of the output of the first function using the bindingstring value.
 9. The non-transitory machine-readable storage medium ofclaim 1, wherein the cryptographic system includes a network of finitestate machines.
 10. The non-transitory machine-readable storage mediumof claim 1, wherein the cryptographic system includes a network oflookup tables.
 11. The non-transitory machine-readable storage medium ofclaim 1, wherein the cryptographic operation is one of advancedencryption system (AES) or data encryption standard (DES).
 12. A methodof producing a cryptographic implementation of a cryptographic operationmapping an input message to an output message in a cryptographic systemthat binds the cryptographic implementation to a binding string value,comprising: receiving information specifying the binding string value;modifying a cryptographic implementation to receive a identifying stringvalue; modifying the cryptographic implementation based upon thereceived information specifying the binding string value so that: when areceived identifying string value is equal to the binding string value,the cryptographic implementation outputs a correct output message,wherein the keyed cryptographic function includes a first lookup tablethat receives the identifying string and an intermediate value of thekeyed cryptographic function and produces an encoded intermediate valuebased upon the identifying string, and wherein the keyed cryptographicfunction includes a second lookup table that receives the encodedintermediate value and produces a decoded intermediate value based uponthe binding string value.
 13. The method of claim 12, wherein when areceived identifying string value is not equal to the binding stringvalue, the cryptographic implementation outputs an incorrect outputmessage.
 14. The method of claim 12, wherein the identifying stringvalue is based upon an identification of the cryptographicimplementation.
 15. The method of claim 12, wherein the identifyingstring value is based upon a hash of a portion of the cryptographicimplementation.
 16. The method of claim 12, wherein the identifyingstring value is based upon an identification of the cryptographicsystem.
 17. The method of claim 12, wherein the identifying string valueis based upon a user password.
 18. The method of claim 12, whereincryptographic implementation includes a plurality of functions includinga first function producing the intermediate value and second function,and modifying the cryptographic implementation so that: a secondfunction is performed on the output of the first function wherein thesecond function includes decoding the output of the first function usingthe binding string value.
 19. The method of claim 12, whereincryptographic implementation includes a plurality of functions includinga first function and second function, and modifying the cryptographicimplementation so that: the lookup table perturbs the intermediate valueusing the identifying string value; and a second function is performedon the encoded output of the first function wherein the second functionincludes compensating for the perturbation of the output of the firstfunction using the binding string value.
 20. The method of claim 12,wherein the cryptographic system includes a network of finite statemachines.
 21. The method of claim 12, wherein the cryptographic systemincludes a network of lookup tables.
 22. The method of claim 12, whereinthe cryptographic operation is one of advanced encryption system (AES)or data encryption standard (DES).
 23. A method of performing acryptographic operation using a cryptographic implementation in acryptographic system, comprising: receiving, by the cryptographicsystem, an identifying string value; receiving, by the cryptographicsystem, an input message; performing, by the cryptographic system, akeyed cryptographic operation mapping the input message into an outputmessage wherein the output message is the correct result when theidentifying string value equals a binding string value, wherein thekeyed cryptographic function includes a first lookup table that receivesthe identifying string and an intermediate value of the keyedcryptographic function and produces an encoded intermediate value basedupon the identifying string, and wherein the keyed cryptographicfunction includes a second lookup table that receives the encodedintermediate value and produces a decoded intermediate value based uponthe binding string value.
 24. The method of claim 23, wherein the outputmessage is an incorrect result when the identifying string does notequal the binding string value.
 25. The method of claim 23, wherein theidentifying string value is based upon an identification of thecryptographic implementation.
 26. The method of claim 23, wherein theidentifying string value is based upon a hash of a portion of code inthe cryptographic system.
 27. The method of claim 23, wherein theidentifying string value is based upon an identification of thecryptographic system.
 28. The method of claim 23, wherein theidentifying string value is based upon a user password.
 29. The methodof claim 23, wherein cryptographic implementation includes a pluralityof functions including a first function producing the intermediate valueand second function, and the method further comprises: performing thesecond function on the output of the first function wherein the secondfunction includes decoding the output of the first function using thebinding string value.
 30. The method of claim 23, wherein cryptographicimplementation includes a plurality of functions including a firstfunction and a second function, and the method wherein the lookup tableperturbs the intermediate value using the identifying string value,further comprising: performing the second function on the perturbedoutput of the first function wherein the second function includescompensating for the perturbation of the output of the first functionusing the binding string value.
 31. The method of claim 23, wherein thecryptographic system includes a network of finite state machines. 32.The method of claim 23, wherein the cryptographic system includes anetwork of lookup tables.
 33. The method of claim 23, wherein thecryptographic operation is one of advanced encryption system (AES) ordata encryption standard (DES).